Algebra II : Setting Up Equations
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Example Questions
Example Question #41 : Setting Up Equations
Set up the equation: Two times a number is equal to one less than the number.
Start by breaking up the details. Let 
Two times a number:
Is equal to:
One less than the number:
Combine all the terms.
The answer is:
Example Question #42 : Setting Up Equations
Set up the following equation: Four times the quantity of two less than a number is eight times the number.
To solve this question, break up the wording by parts.
Quantity of two less than a number:
Four times the quantity of two less than a number:
Is:
Eight times the number:
Combine the terms.
The answer is:
Example Question #43 : Setting Up Equations
A photo company charges a 
To translate this into an expression, it's helpful to identify what the constant is in the problem. In other words, what is not changing no matter how many photos you print? In this case, it's the set-up fee 
Example Question #44 : Setting Up Equations
Set up an equation in terms of a single variable that can be used to solve the problem below.
The area of a rectangular pool is 
None of the above
The area of a rectangular is length times width. So,
If 
The length of the pool is two feet less than twice the width, which means:
Substitute 
so
Example Question #45 : Setting Up Equations
Write the following equation:
Shirts are 15 dollars and jeans are 30 dollars.
The total amount of money you made from selling shirts and jeans is at least 200 dollars.
You know that shirts sell for 15 dollars and jeans sell for 30 dollars.
The tricky part is knowing that you sold at least 200 dollars worth of merchandise.
This means that you could have sold more than 200 dollars, but no less than that.
This means that your answer is
Example Question #41 : Equations
Corey buys potatoes for $2.25 per pound and quinoa for $5.75 per pound. If Corey buys p pounds of potatoes and q pounds of quinoa for $37.25, which of the equations below represents his transaction?
The cost for p pounds of potatoes is 2.25p and the cost for q pounds of quinoa is 5.75q. The total amount Corey pays is the sum of the cost for potatoes and the cost for quinoa.
2.25p + 5.75q = 37.25
Example Question #47 : Setting Up Equations
Write in slope-intercept form
Recall the form for slope-intercept as follows.
where 
Given the equation in this question, first distribute the one fourth to both terms inside the parentheses.
Next, subtract two from both sides to isolate y.
This results in the slope-intercept form of the equation.
Example Question #48 : Setting Up Equations
Beetle A runs in a straight line for 30cm before bumping into Beetle B, who then runs for another 90cm at a rate 3 times faster than Beetle A.
What is the rate of Beetle B?
Unable to determine from the information provided
Knowing:
Beetle A:
Beetle B:
Combined:
Multiply each term by LCD (3x) to get:
Example Question #49 : Setting Up Equations
Set up the equation: The square root of six less than twice a number is equal to nine.
Split up the sentence into parts.
Twice a number:
Six less than twice a number:
The square root of six less than twice a number:
Is equal to nine:
The answer is:
Example Question #138 : How To Find F(X)
Set up the equation: The sum of two times a number and forty is equal to sixteen.
Break up the problem into parts.
Two times a number:
The sum of two times a number and forty:
Is equal to sixteen:
Combine the terms to form the equation.
The answer is:
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